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# In the diagram below, which of the following is always true?

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Joined: 02 Sep 2009
Posts: 52971
In the diagram below, which of the following is always true?  [#permalink]

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06 Mar 2018, 20:56
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In the diagram below, which of the following is always true?

I. a > b
II. c > a
III. d > a

(A) I only
(B) II and III only
(C) I, II, and III
(D) II only
(E) None of these

Attachment:

2018-03-07_0854.png [ 15 KiB | Viewed 808 times ]

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Posts: 52971
Re: In the diagram below, which of the following is always true?  [#permalink]

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06 Mar 2018, 20:57
Bunuel wrote:

In the diagram below, which of the following is always true?

I. a > b
II. c > a
III. d > a

(A) I only
(B) II and III only
(C) I, II, and III
(D) II only
(E) None of these

Attachment:
2018-03-07_0854.png

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Re: In the diagram below, which of the following is always true?  [#permalink]

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06 Mar 2018, 23:41
In the diagram below, which of the following is always true?

I. a > b
II. c > a
III. d > a

From the diagram, we can figure out the below:
a+b = 180
c+d = a

I. a > b
- Not necessarily always bigger than b

II. c > a
c+d = a ( so c is less than a )

III. d > a
c+d = a ( so d is less than a )

The Answer is E
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Joined: 17 Sep 2016
Posts: 5
Re: In the diagram below, which of the following is always true?  [#permalink]

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07 Mar 2018, 01:24
IMHO A.

2 & 3 are wrong, so that rules out all options.

Why A is right?

a+b=180.

b+c+d=180.
c+d=180-b
also b<c+d. properties of triangle.
so b<180-b
so 2b<180. b<90.
a+b=180. so a>b.

Kindly correct if any wrong.
SVP
Joined: 26 Mar 2013
Posts: 2067
Re: In the diagram below, which of the following is always true?  [#permalink]

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07 Mar 2018, 09:46
1
movien wrote:
IMHO A.

2 & 3 are wrong, so that rules out all options.

Why A is right?

a+b=180.

b+c+d=180.
c+d=180-b
also b<c+d. properties of triangle.
so b<180-b
so 2b<180. b<90.
a+b=180. so a>b.

Kindly correct if any wrong.

Can a triangle with b = 120 & c = 20 & d =40 work??............b+ c + d =180.............but here b > a+c

Then, the highlighted is not necessarily true.
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Joined: 17 Sep 2016
Posts: 5
Re: In the diagram below, which of the following is always true?  [#permalink]

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07 Mar 2018, 21:26
Mo2men wrote:
movien wrote:
IMHO A.

2 & 3 are wrong, so that rules out all options.

Why A is right?

a+b=180.

b+c+d=180.
c+d=180-b
also b<c+d. properties of triangle.
so b<180-b
so 2b<180. b<90.
a+b=180. so a>b.

Kindly correct if any wrong.

Can a triangle with b = 120 & c = 20 & d =40 work??............b+ c + d =180.............but here b > a+c

Then, the highlighted is not necessarily true.

Then i Guess the property b<c+d is wrong..
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Re: In the diagram below, which of the following is always true?  [#permalink]

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08 Mar 2018, 16:57
Bunuel wrote:

In the diagram below, which of the following is always true?

I. a > b
II. c > a
III. d > a

(A) I only
(B) II and III only
(C) I, II, and III
(D) II only
(E) None of these

Attachment:
2018-03-07_0854.png

Since the measure of an exterior angle of a triangle must be equal to the sum of the measures of the two remote interior angles, we can create the equation:

a = c + d

Thus a must be greater than c and d. So Roman numerals II and III are definitely incorrect.

If a = 100, then b = 80. But if a = 80, then b = 100, and we see that Roman numeral I is not always true.

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Re: In the diagram below, which of the following is always true?  [#permalink]

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12 Mar 2018, 10:29
movien wrote:
Mo2men wrote:
movien wrote:
IMHO A.

2 & 3 are wrong, so that rules out all options.

Why A is right?

a+b=180.

b+c+d=180.
c+d=180-b
also b<c+d. properties of triangle.
so b<180-b
so 2b<180. b<90.
a+b=180. so a>b.

Kindly correct if any wrong.

Can a triangle with b = 120 & c = 20 & d =40 work??............b+ c + d =180.............but here b > a+c

Then, the highlighted is not necessarily true.

Then i Guess the property b<c+d is wrong..

Hello

The property b < c+d does NOT apply to the angles of a triangle (meaning its not necessary that sum of two angles has to be greater than the third one)
But it DOES apply to the sides of a triangle. So a triangle with sides b, c and d respectively will always have the following:

b+c > d
c+d > b
b+d > c
Re: In the diagram below, which of the following is always true?   [#permalink] 12 Mar 2018, 10:29
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# In the diagram below, which of the following is always true?

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